E. Arrondo, J. Sendra, and J. R. Sendra, Genus formula for generalized offset curves, Journal of Pure and Applied Algebra, vol.136, issue.3, pp.199-209, 1999.
DOI : 10.1016/S0022-4049(98)00028-0

A. Aurenhammer, Power Diagrams: Properties, Algorithms and Applications, SIAM Journal on Computing, vol.16, issue.1, pp.78-96, 1987.
DOI : 10.1137/0216006

L. Chandrajit and . Bajaj, Some applications of constructive real algebraic geometry, Algebraic geometry and its applications, pp.393-405, 1990.

A. John, W. D. Beachy, and . Blair, Abstract Algebra, 1996.

B. Buchberger, G. E. Collins, and B. Kutzler, Algebraic Methods for Geometric Reasoning, Annual Review of Computer Science, vol.3, issue.1, pp.85-119, 1988.
DOI : 10.1146/annurev.cs.03.060188.000505

J. Bochnak, M. Coste, and M. Roy, Real algebraic geometry, 1987.
DOI : 10.1007/978-3-662-03718-8

[. Blum, F. Cucker, M. Shub, and S. Smale, Complexity and real computation, 1998.
DOI : 10.1007/978-1-4612-0701-6

R. Benedetti and J. Risler, Real algebraic and semialgebraic sets, 1990.

B. Buchberger, Ein algorithmisches Kriterium f??r die L??sbarkeit eines algebraischen Gleichungssystems, Aequationes Mathematicae, vol.95, issue.3, pp.374-383, 1970.
DOI : 10.1007/BF01844169

URL : http://www.digizeitschriften.de/download/PPN356261603_0004/PPN356261603_0004___log73.pdf

B. Buchberger, A criterion for detecting unnecessary reductions in the construction of Gröbner-bases, Symbolic and algebraic computation (EUROSAM '79, 1979.

B. Buchberger, Applications of Gröbner bases in nonlinear computational geometry, Mathematical aspects of scientific software, pp.59-87, 1986.

B. Buchberger, Introduction to Groebner Bases, Automata, languages and programming, pp.378-379, 1992.
DOI : 10.1007/978-3-642-59048-1_2

B. Buchberger, Introduction to Groebner Bases, Gröbner bases and applications, pp.3-31, 1998.
DOI : 10.1007/978-3-642-59048-1_2

[. Choi, S. W. Choi, and H. Moon, Mathematical theory of medial axis transform, Pacific Journal of Mathematics, vol.181, issue.1, pp.57-88, 1997.
DOI : 10.2140/pjm.1997.181.57

[. Chen and J. W. Demmel, Balancing sparse matrices for computing eigenvalues, Proceedings of the International Workshop on Accurate Solution of Eigenvalue Problems, pp.261-287, 1998.
DOI : 10.1016/S0024-3795(00)00014-8

F. John, Canny and Ioannis Z. Emiris. A subdivision-based algorithm for the sparse resultant, J. ACM, vol.47, issue.3, pp.417-451, 2000.

D. Cox, J. Little, and D. O. Shea, Ideals, varieties, and algorithms An introduction to computational algebraic geometry and commutative algebra, 1997.

[. Cox, J. Little, and D. O. Shea, Using algebraic geometry
DOI : 10.1007/978-1-4757-6911-1

A. Capani, G. Niesi, and L. Robbiano, CoCoA, a system for doing Computations in Commutative Algebra Available via anonymous ftp from cocoa, 2000.

[. Chen, E. Papadopoulou, and J. Xu, Robust algorithm for k-gon voronoi diagram construction, Abstracts for the Fourteenth Canadian Conference on Computational Geometry CCCG '02, pp.77-81, 2002.

A. Deschamps, Handbook of Aluminum, chapter Analytical Techniques for Aluminium Alloys, Alloy Production and Materials manufacturing, pp.155-192, 2003.

O. Devillers, S. Meiser, and M. Teillaud, The space of spheres, a geometric tool to unify duality results on Voronoi diagrams
URL : https://hal.archives-ouvertes.fr/hal-01180157

Z. Ioannis, J. F. Emiris, and . Canny, Efficient incremental algorithms for the sparse resultant and the mixed volume, J. Symbolic Comput, vol.20, issue.2, pp.117-149, 1995.

Z. Ioannis and . Emiris, On the complexity of sparse elimination, J. Complexity, vol.12, issue.2, pp.134-166, 1996.

. Fau, . Jean-charles-faugère, and . Gb, Available from http

]. R. Fj94a, J. K. Farouki, and . Johnstone, Computing point/curve and curve/curve bisectors, Design and application of curves and surfaces, pp.327-354, 1992.

T. Rida, J. K. Farouki, and . Johnstone, The bisector of a point and a plane parametric curve, Comput. Aided Geom. Design, vol.11, issue.2, pp.117-151, 1994.

T. Rida, C. A. Farouki, and . Neff, Algebraic properties of plane offset curves, Curves and surfaces in CAGD '89 (Oberwolfach, pp.101-127, 1989.

T. Rida, C. A. Farouki, and . Neff, Analytic properties of plane offset curves, Curves and surfaces in CAGD '89 (Oberwolfach, pp.83-99, 1989.

T. Rida, R. Farouki, and . Ramamurthy, Degenerate point/curve and curve/curve bisectors arising in medial axis computations for planar domains with curved boundaries, Comput. Aided Geom. Design, vol.15, issue.6, pp.615-635, 1998.

T. Rida, R. Farouki, and . Ramamurthy, Specified-precision computation of curve/curve bisectors, Internat. J. Comput. Geom. Appl, vol.8, pp.5-6599, 1998.

[. Golden and M. Group, Introductory MACSYMA documentation: a collection of papers: (a) An introduction to ITS for the Macsyma user, (b) ITS easy once ITS explained, and (c) Macsyma primer, 1982.

M. Giusti, Some effectivity problems in polynomial ideal theory, In EUROSAM Lecture Notes in Comput . Sci, vol.84, issue.174, pp.159-171, 1984.
DOI : 10.1007/BFb0032839

[. Greuel and G. Pfister, A Singular introduction to commutative algebra, 2002.
DOI : 10.1007/978-3-662-04963-1

[. Greuel, G. Pfister, and H. Schönemann, Singular 2.0. A Computer Algebra System for Polynomial Computations, 2001.

[. Gröbner, ??ber die algebraischen Eigenschaften der Integrale von linearen Differentialgleichungen mit konstanten Koeffizienten, Monatshefte f??r Mathematik und Physik, vol.47, issue.1, 1939.
DOI : 10.1007/BF01695500

R. Daniel, M. E. Grayson, and . Stillman, Macaulay 2, a software system for research in algebraic geometry

L. Guibas and J. Stolfi, Primitives for the manipulation of general subdivisions and the computation of Voronoi, ACM Transactions on Graphics, vol.4, issue.2, pp.74-123, 1985.
DOI : 10.1145/282918.282923

E. Hansen, Global optimization using interval analysis, volume 165 of Monographs and Textbooks in Pure and Applied Mathematics, 1992.

T. Michael and . Heath, Scientific Computing : An Introductory Survey

. Hù, T. D?ungd?ung, and . Hù-ynh, A superexponential lower bound for Gröbner bases and Church-Rosser commutative Thue systems, Inform. and Control, vol.68, issue.1-3, pp.196-206, 1986.

M. Christoph, P. J. Hoffmann, and . Vermeer, Eliminating extraneous solutions in curve and surface operations, Internat. J. Comput. Geom

[. Kantorovitch, On some further applications of the Newton approximation method

I. Menelaos, I. Z. Karavelas, and . Emiris, Predicates for the Planar Additively Weighted Voronoi Diagram, 2002.

[. Kim, D. Kim, and K. Sugihara, Voronoi Diagram of a Circle Set Constructed from Voronoi Diagram of a Point Set, Algorithms and computation, pp.432-443, 1969.
DOI : 10.1007/3-540-40996-3_37

[. Kim, D. Kim, and K. Sugihara, Voronoi diagram of a circle set from Voronoi diagram of a point set

[. Kim, D. Kim, and K. Sugihara, Voronoi diagram of a circle set from Voronoi diagram of a point set

R. Klein, Concrete and abstract Vorono¨?Vorono¨? diagrams, 1989.

O. Knüppel and . Profil, BIAS?a fast interval library, International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, pp.3-4277, 1993.

A. Nikolaevich and K. , A statistical theory for the recrystallization of metals, Akad. nauk SSSR, Izv., Ser. Matem, vol.1, issue.3, pp.355-359, 1937.

W. Krämer, Verified solution of eigenvalue problems with sparse matrices, Computational and applied mathematics, I (Dublin, pp.277-287, 1991.

[. Li, Numerical Solution of Polynomial Systems by Homotopy Continuation Methods, Handbook of numerical analysis XI, Handb. Numer. Anal., XI, pp.209-304, 2003.
DOI : 10.1016/S1570-8659(02)11004-0

N. Jack, C. B. Little, and . Moler, Matlab ? User's Guide, 1990.

B. Rich, D. C. Lehoucq, C. Sorensen, and . Yang, ARPACK users' guide. Software, Environments, and Tools, Society for Industrial and Applied Mathematics (SIAM), 1998.

[. Mercier and O. Baujard, Voronoi diagrams to model forest dynamics in french guiana, Proceedings of GeoComputation '97 & Sirc '97, pp.161-171, 1997.

J. Merlet, Some algebraic geometry problems arising in the field of mechanism theory, Algorithms in algebraic geometry and applications, pp.271-283, 1994.
DOI : 10.1007/978-3-0348-9104-2_13

J. Merlet, Alias: an interval analysis based library for solving and analyzing system of equations, SEA, pp.14-16, 2000.

J. Merlet, A Parser for the Interval Evaluation of Analytical Functions and its Application to Engineering Problems, Journal of Symbolic Computation, vol.31, issue.4, pp.475-486, 2001.
DOI : 10.1006/jsco.2000.0429

[. Mioc, The Voronoi spatio-temporal data structure, 2002.

[. Möller and F. Mora, Upper and lower bounds for the degree of Groebner bases, In EUROSAM Lecture Notes in Comput. Sci, vol.84, issue.174, pp.172-183, 1984.
DOI : 10.1007/BFb0032840

R. E. Moore, A Test for Existence of Solutions to Nonlinear Systems, SIAM Journal on Numerical Analysis, vol.14, issue.4
DOI : 10.1137/0714040

[. Mourrain, Enumeration problems in geometry, robotics and vision, Algorithms in algebraic geometry and applications, pp.285-306, 1994.
DOI : 10.1007/978-3-0348-9104-2_14

L. Jorgen and . Nikolajsen, An improved Laguerre eigensolver for unsymmetric matrices, SIAM J. Sci. Comput, vol.22, issue.3, pp.822-834, 2000.

A. Okabe, B. Boots, and . Sugihara, Spatial tessellations: concepts and applications of Vorono¨?Vorono¨? diagrams, 1992.

[. Colm´o-'dúnlaing, M. Sharir, and C. Yap, Generalized voronoi diagrams for moving a ladder. I: Topological analysis, Communications on Pure and Applied Mathematics, vol.4, issue.4, pp.423-483, 1986.
DOI : 10.1002/cpa.3160390402

[. Colm´o-'dúnlaing, M. Sharir, and C. Yap, Generalized Voronoi diagrams for a ladder: II. Efficient construction of the diagram, Algorithmica, vol.25, issue.1-4, pp.27-59, 1987.
DOI : 10.1007/BF01840348

[. Colm´o, C. Dúnlaing, and . Yap, A " retraction " method for planning the motion of a disc, J. Algorithms, vol.6, issue.1, pp.104-111, 1985.

G. Pini, LEFTMOST EIGENVALUE OF REAL AND COMPLEX SPARSE MATRICES ON PARALLEL COMPUTER USING APPROXIMATE INVERSE PRECONDITIONING, Parallel Algorithms and Applications, vol.1, issue.1, pp.41-58, 2002.
DOI : 10.1137/0913035

[. Ramamurthy and R. T. Farouki, Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I. Theoretical foundations, Journal of Computational and Applied Mathematics, vol.102, issue.1, pp.119-141, 1999.
DOI : 10.1016/S0377-0427(98)00211-8

URL : http://doi.org/10.1016/s0377-0427(98)00211-8

R. Ramamurthy and R. T. Farouki, Voronoi diagram and medial axis algorithm for planar domains with curved boundaries ??? II: Detailed algorithm description, Journal of Computational and Applied Mathematics, vol.102, issue.2, pp.253-277, 1999.
DOI : 10.1016/S0377-0427(98)00223-4

URL : http://doi.org/10.1016/s0377-0427(98)00223-4

. Rou-]-fabrice-rouillier and . Realsolving, Available from http://spaces.lip6.fr/ rouillie

I. R. Shafarevich, Basic algebraic geometry Varieties in projective space, Translated from the, 1988.

C. Voiron-canicio, Analyse spatiale et analyse d'images par la morphologie mathématique, RECLUS, 1990.

[. Vorono¨?vorono¨?, Nouvelles applications des paramètres continusàcontinusà la théorie des formes quadratiques. premier mémoire. sur quelques propriétés des formes quadratiques positives parfaites, Journal für die reine und angewandte Mathematik, pp.97-178, 1907.

[. Vorono¨?vorono¨?, Nouvelles applications des paramètres continusàcontinusà la théorie des formes quadratiques.deuxì eme mémoire. recherches sur lesparallélò edres primitifs.premì ere partie. partition uniforme de l'espace analytiquè a n dimensionsàdimensionsà l'aide des translations d'un même polyèdre convexe, Journal für die reine und angewandte Mathematik, pp.198-287, 1908.

[. Vorono¨?vorono¨?, Nouvelles applications des paramètres continusàcontinusà la théorie des formes quadratiques.deuxì eme mémoire. recherches sur lesparallélò edres primitifs. seconde partie. domaines de formes quadratiques correspondant aux différents types deparallélò edres primitifs, Journal für die reine und angewandte Mathematik, pp.67-181, 1910.

-. Chee and . Yap, An O(n log n) algorithm for the Vorono? ? diagram of a set of simple curve segments, Discrete Comput. Geom, vol.2, issue.4, pp.365-393, 1987.

A. Implicit, r 2 ? p 2 ) * y 4 ? 16 * p * x 3 * y 2 ? 8 * (r 2 ? 4 * p 2 ) * x 2 * y 2 + -8*r*(a*x-b*y+c)^2*(b*x+a*y+d)^2+32*o^2*(a*x-b*y+c, p.2

. Delaunay-graph-predicate, 43 field, 68, 81 generalised offset, pp.19-21